Further calculations for the McKean stochastic game for a spectrally negative levy process: from a point to an interval

Baurdoux, Erik J. and Van Schaik, K.
(2011)
Further calculations for the McKean stochastic game for a spectrally negative levy process: from a point to an interval.
Journal of Applied Probability, 48
(1).
pp. 200-216.
ISSN 0021-9002

Abstract

Following Baurdoux and Kyprianou (2008) we consider the McKean stochastic game, a game version of the McKean optimal stopping problem (American put), driven by a spectrally negative Levy process. We improve their characterisation of a saddle point for this game when the driving process has a Gaussian component and negative jumps. In particular, we show that the exercise region of the minimiser consists of a singleton when the penalty parameter is larger than some threshold and 'thickens' to a full interval when the penalty parameter drops below this threshold. Expressions in terms of scale functions for the general case and in terms of polynomials for a specific jump diffusion case are provided.